Culture, psychology and physiology (gender) all play an important role is determining ones willingness and ability to compete.
In one sense your nationality influences your desire to compete. Competition and conflict does not originate with Americans but we have fostered via our culture a society of those who compete. Human nature outside of modern social forces was largely communal and cooperative based.
Psychologically speaking on an individual basis what techniques you know to handle competition will help you perform under the stress of competition but will not itself cause you to be a better performer. It seems the challenge or resistance causes development; not competition.
Testosterone and the male gender roles make competition easier for men. Men are less anxious to start competition. Being easier to start will cause more men to engage in competitive behavior than woman. (Even though women are equally competitive once they begin). Men also outperform women on higher competitive test like college entrance exams where as women outperform men on high school exit exams.
(a) attitudes toward competition (although men may feel comfortable performing in a competitive setting, women may be more anxious about such prospects), (b) beliefs about relative performance (men may be more confident that they are among the highest-performing participants and thus be more inclined to compete), and (c) risk and feedback aversion (the tournament is not only competitive but is also more uncertain and provides more information about relative performance than the piece-rate scheme; if women are more averse to such factors, they may be less inclined to select
-Gender and Competition: Why do woman shy away from competition.